Question

The multiplicative inverse of additive inverse of\[ - 8\] is:
A). \[\dfrac{1}{8}\]
B). \[8\]
C). \[0\]
D). \[16\]\[\]

Answer 1

Hint: Here, in the given question we are asked to find the multiplicative inverse of additive inverse of\[ - 8\]. The word “inverse” represents something that is opposite in effect. To find the desired result, first we will find the additive inverse of the given number and then the multiplicative inverse of the result of additive inverse.

Complete step-by-step solution:
As we know that, when a number is added to its additive inverse, the result is always zero. So, we have to find a number whose sum with \[ - 8\] comes out to be zero.
Therefore, additive inverse of\[ - 8\] will be\[8\]
Multiplicative inverse of a number is also known as reciprocal. Also, we know that when a reciprocal is multiplied to the given number, the result is always one. So, we have to find a number whose multiplication with \[8\] comes out to be\[1\].
Therefore, multiplicative inverse of \[8\] will be \[\dfrac{1}{8}\]
Hence, the multiplicative inverse of the additive inverse of\[ - 8\] is \[\dfrac{1}{8}\].
Hence the answer is option A. \[\dfrac{1}{8}\]
Additional information: There is no difference if the order of inverse changes. In other words, the result will always be the same if we find multiplicative inverse of additive inverse of a number or additive inverse of multiplicative inverse of a number.

Note: Simply, we can find the additive inverse just by changing the sign of the given number. and multiplicative inverse by flipping the fraction or swapping the numerator and denominator. In multiplicative inverse, sign of a number does not change. It remains the same as given.